The length of the largest continuous interval in which the function `f(x)=4x-tan2x` is monotonic is `pi/2` (b) `pi/4` (c) `pi/8` (d) `pi/(16)`

The length of the longest interval in which the function 3sinx-4sin^3x is increasing is pi/3 (b) pi/2 (c) (3pi)/2 (d) pi

The value of k(k >0) such that the length of the longest interval in which the function f(x)=sin^(-1)|sink x|+cos^(-1)(cosk x) is constant is pi/4 is/ are (a)8 (b) 4 (c) 12 (d) 16

The angles at which the circles (x-1)^2+y^2=10a n dx^2+(y-2)^2=5 intersect is pi/6 (b) pi/4 (c) pi/3 (d) pi/2

The angle between the tangents to the parabola y^2=4a x at the points where it intersects with the line x-y-a=0 is (a) pi/3 (b) pi/4 (c) pi (d) pi/2

Find the intervals of decrease and increase for the function f(x)=cos(pi/x)

The value of c in Lagranges theorem for the function f(x)=logsinx in the interval [pi/6,(5pi)/6] is (a) pi/4 (b) pi/2 (c) (2pi)/3 (d) none of these

The maximum value of the function f(x)=sin(x+pi/6)+cos(x+pi/6) in the interval (0,pi/2) occurs at pi/(12) (b) pi/6 (c) pi/4 (d) pi/3

The sum of all the solution in [0,4pi] of the equation tanx+cotx+1=cos(x+pi/4)i s (a) 3pi (b) pi/2 (c) (7pi)/2 (d) 4pi

IF the lengths of the side of triangle are 3,5A N D7, then the largest angle of the triangle is pi/2 (b) (5pi)/6 (c) (2pi)/3 (d) (3pi)/4

On which of the following intervals is the function x^(100)+sinx-1 decreasing? (a) (0,pi/2) (b) (0,1) (c) (pi/2,pi) (d) none of these